Memristive devices, or memristors, are a new type of switching devices with an electrically switchable device resistance. Memristive devices are both scientifically and technically interesting, and hold promise for non-volatile memory (NVM) and other fields. As today's flash memory technology is reaching its scaling limit, there is an urgent need for new memory technologies that can meet the storage capacity and speed demanded by future applications, and memories using resistive switching devices, such as memristors, are a promising candidate for meeting that need. For NVM applications, many nanoscale resistive switching devices can be formed in a two-dimensional array, such as a crossbar structure, to provide a very high storage capacity. Nevertheless, it has been a major challenge to reliably read the resistive state of a selected resistive switching device in an array, due that existence of other switching devices in the array that may form paths for leakage current, which can significantly reduce the signal/noise ratio of the read operation.